A016217 Expansion of 1 / ((1-x) * (1-3*x) * (1-12*x)).

1, 16, 205, 2500, 30121, 361816, 4342885, 52117900, 625424641, 7505125216, 90061591165, 1080739359700, 12968873113561, 155626479754216, 1867517764225045, 22410213192223900, 268922558371256881, 3227070700648792816, 38724848408366644525, 464698180902143126500

Offset

0,2

Links

Table of n, a(n) for n=0..19.

Index entries for linear recurrences with constant coefficients, signature (16, -51, 36).

Formula

a(0)=1, a(1)=16, a(n)=15*a(n-1)-36*a(n-2)+1. - Vincenzo Librandi, Feb 10 2011

a(0)=1, a(1)=16, a(2)=205, a(n)=16*a(n-1)-51*a(n-2)+36*a(n-3). - Harvey P. Dale, May 06 2012

a(n) = 1/22-(1/2)*3^n+(16/11)*12^n. - Antonio Alberto Olivares, May 12 2012

Maple

a:= n-> add((12^(n+1-j)-3^(n+1-j))/9, j=0..n): seq(a(n), n=0..20); # Zerinvary Lajos, Jan 12 2007

Mathematica

CoefficientList[Series[1/((1-x)(1-3x)(1-12x)), {x, 0, 30}], x] (* or *) LinearRecurrence[{16, -51, 36}, {1, 16, 205}, 30] (* Harvey P. Dale, May 06 2012 *)

Prog

(PARI) a(n)=1/22-1/2*3^n+16/11*12^n \\ Charles R Greathouse IV, Jun 01 2026

Crossrefs

Sequence in context: A238282 A161729 A157707 * A055758 A046088 A186853

Adjacent sequences: A016214 A016215 A016216 * A016218 A016219 A016220

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved